The primary source on Favored Enemy is either Player’s Handbook in the ranger class description, or Rules Compendium if you buy its assertion of primacy. The descriptions in the Invisibility description in Dungeon Master’s Guide, Improved Manyshot in Epic Level Handbook, or even darkness, despite also being in the Player’s Handbook, are definitely not the primary source on Favored Enemy.
Further caveats, limitations, and addenda not mentioned in the primary source description are contradictions with that description. If Favored Enemy had defined itself as precision damage, the primary source on precision damage would apply, but it didn’t, which means that neither the precision damage description nor anywhere else can define it as such.
I would be inclined, in general, to follow contradictory rules as far as they go. Darkness and Invisibility cannot define Favored Enemy as precision damage in general, but it can say Favored Enemy doesn’t work in those conditions. Here, specific-trumps-general: rather than trying to redefine what Favored Enemy is (in which primacy asserts itself), they can define a special case which acceptably contradicts the general rules. So my reading of the rules as written would be that Favored Enemy is not precision damage, but it does fail to work in cases of darkness or Invisibility, and does apply only once to Improved Manyshot.
Ultimately, however, I would mostly ignore any and all rules as written that apply any more needless limitations on Favored Enemy. Of all the iconic core class features,1 Favored Enemy is one of the weakest, and that’s even assuming that it “just works” on any and all attacks against the designated foes (including, therefore, Improved Manyshot).
- Slow fall and wild empathy, if counted as “iconic class features,” are definitely weaker than favored enemy, and smite evil and trapfinding give it a run for its money too. That’s still a small list compared to all of the options.
It really depends on how your DM runs the campaign and how your party decides to proceed.
It's not possible to give you an itemized breakdown because I am familiar with SKT as a player, not a DM, and your campaign experience will be unique. That said, as laid out by the book:
Humanoids appear very frequently because you will encounter them both in towns and while out adventuring.
Beasts also appear fairly regularly, but not as often as humans.
There are some Monstrosities as well. They are nowhere near as common as humanoids or beasts but, unit for unit, they tend to be more dangerous.
You're likely to encounter some Undead but this is highly variable and depends on your party's direction.
We had a trivial amount of Fey in our SKT campaign but I believe it was something the DM added in specifically for one of the character's backstory.
Best Answer
The most numerous Favoured Enemy is Humanoids, and the most numerous Greater Enemy is Constructs in DOTMM
Using the link you provided for the population per level, I made a table of how often each unique creature appears on each level with the DOTMM. I did not include the number of each creature as I thought this may tilt the count towards types with more lower CR creatures in them.
Favoured Enemy
As you can see from the chart above, Humanoids are by far the most numerous Favoured Enemy Type in DOTMM, with Undead second, and Monstrosities third. In my opinion, either one of these three would be fine to pick, as there is a larger number of Humanoids that you may not even fight, as this list includes all possible encounters. A large number of these humanoids you can choose to just ignore, or possibly talk your way out of a fight.
It is also important to remember that only the Revised Ranger is able to pick Humanoid as it's Favoured Enemy. For anyone playing a regular ranger, you will be unable to pick Humanoids.
Also, some of these enemies are low CR, so may just be blown up by a well placed fireball before your ranger gets to attack.
Greater Favoured Enemy
The Greater Favoured Enemy list is much closer in terms of the top three, which are Constructs, Aberrations, and Fiends. Each have a similar distribution of CR levels as well, so this one really comes down to personal preference. There is a slightly higher number of high CR Fiends, though not enough to make it obviously better to pick Fiends over Constructs of Aberrations.
Ultimately, it depends on what the player prefers
It is quite hard to pick one obviously right choice, as what you encounter ultimately depends on what your DM throws at you, and which paths/places the party spends more time in. In my opinion, any one of the top three for each group of favoured enemy will be your best choices.